Problem with Wolfram's online integrator

BenVitale

I tried to do integral[cos(x)]^x dx

but Wolfram's online integrator reported that it couldn't do it

Am I missing something?

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Dale

Mentor
From your syntax it is not clear if you want to take the integral of cos(x)^x or if you want to take the integral of cos(x) and then raise that to the power of x. If it is the first then there is probably no known closed form solution for that integral.

dE_logics

Wolfram is not that good.

Try www.quickmath.com, it's better; or if you're on Linux, there're plenty of computer algebra systems.

However this time quickmath also failed...very hilarious answer.

$$\int \sp{\displaystyle x} {{{\cos \left( { \%M} \right)} \sp \%M} \ {d \%M}}$$

yacas gives the same results (as quickmath).

sympy takes infinite time to solve (as with most complex cases)

So I conclude there's something wrong with the question itself.

BenVitale

From your syntax it is not clear if you want to take the integral of cos(x)^x or if you want to take the integral of cos(x) and then raise that to the power of x.
.
It's taking the integral of cos(x)^x

So I conclude there's something wrong with the question itself.
Maybe, maybe not. I thought of a manipulation:

I figure that for all values of x, cos x will fall in [-1,+1].
So, taking the integral of cos(x)^x is equivalent to taking the integral of x^x over [-1,0] and [0,+1]

What do you think?

Dale

Mentor
By that logic the integral would be the same as sin(x)^x or frac(x)^x or saw(x)^x or any other function bounded between -1 and 1.

BenVitale

By that logic the integral would be the same as sin(x)^x or frac(x)^x or saw(x)^x or any other function bounded between -1 and 1.
Oh, yes. I see your point. I'm at loss here. What do you suggest?

Dale

Mentor
I believe there is no closed form for this integral. You will have to evaluate it numerically.

"Problem with Wolfram's online integrator"

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